Euler and the partial sums of the prime harmonic series

  title={Euler and the partial sums of the prime harmonic series},
  author={P. Pollack},
  journal={Elemente Der Mathematik},
  • P. Pollack
  • Published 2015
  • Mathematics
  • Elemente Der Mathematik
Abstract. In a 1737 paper, Euler gave the first proof that the sum of the reciprocals of the prime numbers diverges. That paper can be considered as the founding document of analytic number theory, and its key innovation — socalled Euler products — are now ubiquitous in the field. In this note, we probe Euler’s claim there that “the sum of the reciprocals of the prime numbers” is “as the logarithm” of the sum of the harmonic series. Euler’s argument for this assertion falls far short of modern… Expand
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